In this work, we approximated a set of unknown physical parameters for a semi-empirical mathematical model of a PEMFC. We used an Estimation of Distribution Algorithm (EDA) known as $UMD{A}^G$ to find the tuple that best reproduces the experimental polarization curve. We tackled non-derivable objective functions to perform robust parameter estimation. We compared the sum of the squared error with published results, and the sum and the median of the absolute error values were used to diminish or remove the effect of possible noise or outliers. Since the $UMD{A}^G$ requires a single user-given parameter (the population size) and presents a natural reduction of the variance, it was possible to introduce a variance-based stopping criterion. The obtained results were compared with the most up-to-date evolutionary algorithms, demonstrating that this proposal is competitive. We used four previously reported experimental datasets to get the parameters or validate them. Two of them were used to test the method and to compare it with reported results of recent bio-inspired metaheuristics. Then, we used the identified parameters to simulate the cases of the remaining data sets validating the correct estimation. Finally, we introduced a posterior statistical analysis (hypothesis test), which provided further information about dependencies and the impact of each parameter on the cell performance.

在这项工作中，我们为PEMFC的半经验数学模型近似了一组未知的物理参数。我们使用了一种称为“分布算法估计”（EDA）的方法，$ü\mathrm{中号}d{\mathrm{一种}}^G$找到最能重现实验极化曲线的元组。我们处理了不可导出的目标函数以执行可靠的参数估计。我们将平方误差的总和与已发布的结果进行了比较，并且使用绝对误差值的总和和中值来减少或消除可能的噪声或异常值的影响。自从$ü\mathrm{中号}d{\mathrm{一种}}^G$由于需要单个用户提供的参数（总体大小）并自然减少了方差，因此有可能引入基于方差的停止标准。将获得的结果与最新的进化算法进行比较，表明该建议具有竞争力。我们使用了先前报告的四个实验数据集来获取参数或对其进行验证。他们中的两个被用来测试该方法，并将其与最近的生物启发式元启发式方法的报告结果进行比较。然后，我们使用识别出的参数来模拟验证正确估计的其余数据集的情况。最后，我们介绍了后验统计分析（假设检验），它提供了有关依存关系以及每个参数对电池性能的影响的进一步信息。